Semimedial Near Rings

Objectives: To define the term ‘semimediality’ in the near ring and to demonstrate its presence with an example and to employ several attributes in near rings to analyse its features. Methods: Semimedial near rings are examined in terms of their characteristics using commutativity, distributivity and regular property. The distinction is observed using the concept of homomorphism. Findings: Every near ring which is weak commutative is proved to be semimedial and the converse exists with some additional axioms. The semimedial near ring’s anti-homomorphic image is also observed. Additionally, the correlation between the semimedial near ring and the reduced property is identified. Novelty: This study provides a novel method to medial near ring, which is the semimedial near ring.